NUCLEAR SPIN RELAXATION IN GASES AND LIQUIDS: I. CORRELATION FUNCTIONS

Abstract

Calculation of nuclear spin–lattice relaxation times T₁ in liquids and gases involves the correlation functions of the matrix elements between different spin states of the interaction coupling the nuclear spin to other degrees of freedom of the system. The correlation functions are expressed in terms of a time-dependent pair-distribution function (TDPDF) for the system. The TDPDF is evaluated using the Wigner distribution function to describe the equilibrium ensemble of the gas or liquid. A time expansion of the dynamics of the system to a constant acceleration approximation and use of the symmetry properties of the TDPDF leads to an expression of the form[Formula: see text]This form for the TDPDF is derived for the high temperature dilute gas, for the dilute gas with first quantum correction, and for classical liquids in which the molecular dynamics can be described by the Langevin equation. The quantity g(R) is the radial distribution function appropriate to each case. The quantity P(R², R′², t) is the free particle TDPDF for the classical gas; it is the classical free particle TDPDF at an effective temperature for the quantum gas; it is the product of solutions to the diffusion equation for the liquid multiplied by the (density)².